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PS: Out of SnapPy (2.8) CensusKnots, 1267 were single cusp and for only 81 were the difference between cusp shapes not integers.

One more question: when I ask SnapPy for the cusp shape with and without specifying shortest peripheral curve, the answers seem to differ by an integer. For 5_2, the integer was 2; for 6_1 it is also 2; for 6_2, it is 7. And when I compute the cusp shape for m004, my answer is exactly 2 greater than SnapPy's. Is there a simple reason for this (i.e., is the shape defined mod Z)?

In reference to Sam Nead's answer:

For this I get 0.479646 + 2.91505 I. In checking this with SnapPy (which gives a cusp shape of -2.4902446675 + 2.9794470665 I), I noticed that, while I got the same tetrahedra shapes as Takahashi, SnapPy disagrees with those (my y is the difference between SnapPy's first two shapes). Further, https://knotinfo.math.indiana.edu gives translations yielding a cusp shape of 2.49024 - 2.97945 I. I am assuming this is simply a choice of orientation (the real part of the meridian differs by a sign). When I followed Yokota, I got SnapPy's result. I know that there can exist inequivalent cusp tilings, but it seems to me that the tetrahedra shapes should be invariant, and certainly the cusp shape is an invariant. I am now pretty much thoroughly confused.

Edit:

In reference to Sam Nead's answer:

For this I get 0.479646 + 2.91505 I. In checking this with SnapPy (which gives a cusp shape of -2.4902446675 + 2.9794470665 I), I noticed that, while I got the same tetrahedra shapes as Takahashi, SnapPy disagrees with those (my y is the difference between SnapPy's first two shapes). Further, https://knotinfo.math.indiana.edu gives translations yielding a cusp shape of 2.49024 - 2.97945 I. I am assuming this is simply a choice of orientation (the real part of the meridian differs by a sign). When I followed Yokota, I got SnapPy's result. I know that there can exist inequivalent cusp tilings, but it seems to me that the tetrahedra shapes should be invariant, and certainly the cusp shape is an invariant. I am now pretty much thoroughly confused.

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